You'll need 8 wide mouth pint-size jars, metal rings and lids. Sterilize jars, lids and rings according to manufacturer's directions. Grease inside of jars well. Beat together mayonnaise and half of the sugar until fluffy. Add the eggs and remaining sugar, vanilla, food coloring and applesauce. Sift dry ingredients together and add to the applesauce mixture a little at at time: beat well after each addition. Pour slightly less than one cup of batter into each jar and carefully remove any batter from the rims. Place jars in a preheated 325 degree oven and bake for 40 minutes. While the cakes are baking bring a saucepan of water to a boil and carefully add jar lids. Remove pan from heat and keep lids hot until ready to use. When cakes have finished baking, remove from oven. Make sure each jar rim are clean. Place lids on jars, and screw rings on tightly. Jars will seal as they cool. Cakes will slide right out when ready to use. Unsealed jars should be stored in the refrigerator and eaten within 2 weeks. Sealed jars may be stored with other canned food or placed in a freezer. A properly sealed jar will stay fresh for one year. The cake is safe to eat as long as the jar remains vacuum sealed and free from mold.